LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Results (1-50 of 192 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-12e3-1728.1019-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1019	$0$	✓	✓	$-0.0839$	$0$	$0.730459$	Character $\chi_{1728}(1019, \cdot)$
1-12e3-1728.1021-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1021	$0$	✓	✓	$0.125$	$0$	$1.14899$	Character $\chi_{1728}(1021, \cdot)$
1-12e3-1728.1067-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1067	$0$	✓	✓	$-0.384$	$0$	$0.455713$	Character $\chi_{1728}(1067, \cdot)$
1-12e3-1728.1069-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1069	$0$	✓	✓	$-0.156$	$0$	$0.592045$	Character $\chi_{1728}(1069, \cdot)$
1-12e3-1728.1091-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1091	$0$	✓	✓	$-0.281$	$0$	$0.671455$	Character $\chi_{1728}(1091, \cdot)$
1-12e3-1728.1093-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1093	$0$	✓	✓	$0.490$	$0$	$1.42391$	Character $\chi_{1728}(1093, \cdot)$
1-12e3-1728.11-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.11	$0$	✓	✓	$0.374$	$0$	$1.50008$	Character $\chi_{1728}(11, \cdot)$
1-12e3-1728.1139-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1139	$0$	✓	✓	$-0.249$	$0$	$0.124979$	Character $\chi_{1728}(1139, \cdot)$
1-12e3-1728.1141-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1141	$0$	✓	✓	$0.0410$	$0$	$0.980389$	Character $\chi_{1728}(1141, \cdot)$
1-12e3-1728.1163-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1163	$0$	✓	✓	$0.0410$	$0$	$0.684554$	Character $\chi_{1728}(1163, \cdot)$
1-12e3-1728.1165-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1165	$0$	✓	✓	$0.0839$	$0$	$0.938977$	Character $\chi_{1728}(1165, \cdot)$
1-12e3-1728.1211-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1211	$0$	✓	✓	$-0.00983$	$0$	$1.03797$	Character $\chi_{1728}(1211, \cdot)$
1-12e3-1728.1213-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1213	$0$	✓	✓	$-0.115$	$0$	$0.817068$	Character $\chi_{1728}(1213, \cdot)$
1-12e3-1728.1235-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1235	$0$	✓	✓	$0.00983$	$0$	$0.744650$	Character $\chi_{1728}(1235, \cdot)$
1-12e3-1728.1237-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1237	$0$	✓	✓	$-0.218$	$0$	$0.481859$	Character $\chi_{1728}(1237, \cdot)$
1-12e3-1728.1283-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1283	$0$	✓	✓	$0.458$	$0$	$0.0128604$	Character $\chi_{1728}(1283, \cdot)$
1-12e3-1728.1285-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1285	$0$	✓	✓	$0.249$	$0$	$1.33820$	Character $\chi_{1728}(1285, \cdot)$
1-12e3-1728.13-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.13	$0$	✓	✓	$0.0839$	$0$	$0.779536$	Character $\chi_{1728}(13, \cdot)$
1-12e3-1728.1307-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1307	$0$	✓	✓	$0.249$	$0$	$1.14909$	Character $\chi_{1728}(1307, \cdot)$
1-12e3-1728.1309-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1309	$0$	✓	✓	$-0.0410$	$0$	$1.12171$	Character $\chi_{1728}(1309, \cdot)$
1-12e3-1728.131-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.131	$0$	✓	✓	$0.458$	$0$	$1.57070$	Character $\chi_{1728}(131, \cdot)$
1-12e3-1728.133-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.133	$0$	✓	✓	$-0.0839$	$0$	$0.696688$	Character $\chi_{1728}(133, \cdot)$
1-12e3-1728.1355-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1355	$0$	✓	✓	$-0.218$	$0$	$0.729961$	Character $\chi_{1728}(1355, \cdot)$
1-12e3-1728.1357-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1357	$0$	✓	✓	$-0.490$	$0$	$1.39835$	Character $\chi_{1728}(1357, \cdot)$
1-12e3-1728.1379-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1379	$0$	✓	✓	$-0.115$	$0$	$0.727088$	Character $\chi_{1728}(1379, \cdot)$
1-12e3-1728.1381-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1381	$0$	✓	✓	$0.490$	$0$	$1.83026$	Character $\chi_{1728}(1381, \cdot)$
1-12e3-1728.1427-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1427	$0$	✓	✓	$0.0839$	$0$	$0.617891$	Character $\chi_{1728}(1427, \cdot)$
1-12e3-1728.1429-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1429	$0$	✓	✓	$-0.458$	$0$	$0.0801688$	Character $\chi_{1728}(1429, \cdot)$
1-12e3-1728.1451-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1451	$0$	✓	✓	$-0.458$	$0$	$0.326111$	Character $\chi_{1728}(1451, \cdot)$
1-12e3-1728.1453-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1453	$0$	✓	✓	$-0.249$	$0$	$0.354586$	Character $\chi_{1728}(1453, \cdot)$
1-12e3-1728.1499-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1499	$0$	✓	✓	$-0.00983$	$0$	$0.657909$	Character $\chi_{1728}(1499, \cdot)$
1-12e3-1728.1501-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1501	$0$	✓	✓	$-0.281$	$0$	$0.358007$	Character $\chi_{1728}(1501, \cdot)$
1-12e3-1728.1523-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1523	$0$	✓	✓	$0.343$	$0$	$0.949942$	Character $\chi_{1728}(1523, \cdot)$
1-12e3-1728.1525-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1525	$0$	✓	✓	$-0.384$	$0$	$1.73655$	Character $\chi_{1728}(1525, \cdot)$
1-12e3-1728.155-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.155	$0$	✓	✓	$-0.0839$	$0$	$0.340383$	Character $\chi_{1728}(155, \cdot)$
1-12e3-1728.157-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.157	$0$	✓	✓	$-0.374$	$0$	$0.119050$	Character $\chi_{1728}(157, \cdot)$
1-12e3-1728.1571-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1571	$0$	✓	✓	$-0.374$	$0$	$0.245852$	Character $\chi_{1728}(1571, \cdot)$
1-12e3-1728.1573-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1573	$0$	✓	✓	$-0.0839$	$0$	$0.799260$	Character $\chi_{1728}(1573, \cdot)$
1-12e3-1728.1595-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1595	$0$	✓	✓	$-0.0839$	$0$	$0.500049$	Character $\chi_{1728}(1595, \cdot)$
1-12e3-1728.1597-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1597	$0$	✓	✓	$0.458$	$0$	$0.239970$	Character $\chi_{1728}(1597, \cdot)$
1-12e3-1728.1643-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1643	$0$	✓	✓	$-0.384$	$0$	$0.236810$	Character $\chi_{1728}(1643, \cdot)$
1-12e3-1728.1645-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1645	$0$	✓	✓	$-0.490$	$0$	$1.66960$	Character $\chi_{1728}(1645, \cdot)$
1-12e3-1728.1667-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1667	$0$	✓	✓	$0.384$	$0$	$1.34061$	Character $\chi_{1728}(1667, \cdot)$
1-12e3-1728.1669-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1669	$0$	✓	✓	$0.156$	$0$	$1.28377$	Character $\chi_{1728}(1669, \cdot)$
1-12e3-1728.1715-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1715	$0$	✓	✓	$0.0839$	$0$	$0.910907$	Character $\chi_{1728}(1715, \cdot)$
1-12e3-1728.1717-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.1717	$0$	✓	✓	$0.374$	$0$	$1.02896$	Character $\chi_{1728}(1717, \cdot)$
1-12e3-1728.203-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.203	$0$	✓	✓	$0.115$	$0$	$1.17733$	Character $\chi_{1728}(203, \cdot)$
1-12e3-1728.205-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.205	$0$	✓	✓	$-0.156$	$0$	$0.693358$	Character $\chi_{1728}(205, \cdot)$
1-12e3-1728.227-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.227	$0$	✓	✓	$0.218$	$0$	$1.24645$	Character $\chi_{1728}(227, \cdot)$
1-12e3-1728.229-r0-0-0	$8.02$	$8.02$	$1$	$2^{6} \cdot 3^{3}$	1728.229	$0$	✓	✓	$0.490$	$0$	$0.257014$	Character $\chi_{1728}(229, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.